There is no difference in the measurement of the probe itself!
All probes generate the same millivolts (mV) whether they are in a carbon- or oxygen-rich atmosphere. It is the calculation downstream of the measurement that allows the calculation of either %C, in the heat treatment field, or %O2 in other fields.
It should be noted that the probes intended for the measurement of oxygen (%O2) have electrodes that are not resistant to carburising atmospheres (with carbon). For this reason, these probes cannot be used in the field of heat treatment.
The opposite is not the case. A probe for heat treatment (%C) can be used in an oxygen measurement process, but up to a maximum temperature of 1100°C, above which the metal electrode will melt.